Hindu calendar

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Most of the Hindu calendars are inherited from a system first enunciated in Vedāṅga Jyotiṣa of Lagadha, a late BC adjunct to the Vedas, standardized in the Sūrya Siddhānta (3rd century) and subsequently reformed by astronomers such as Āryabhaṭa (AD 499), Varāhamihira (6th century) and Bhāskara II (12th century). Differences and regional variations abound in these computations, but the following is a general overview of the Hindu lunisolar calendar.

The term -vāsara is often realized as vāra or vaar in Sanskrit-derived and influenced languages. There are many variations of the names in the regional languages, mostly using alternate names of the celestial bodies involved.

The ecliptic is divided into 27 Nakṣatras, which are variously called lunar houses or asterisms. These reflect the moon's cycle against the fixed stars, 27 days and 7¾ hours, the fractional part being compensated by an intercalary 28th nakṣatra titled Abhijit. Nakṣatra's computation appears to have been well known at the time of the Ṛigveda (2nd–1st millennium BC).

The ecliptic is divided into the nakṣatras eastwards starting from a reference point which is traditionally a point on the ecliptic directly opposite the star Spica called Citrā in Sanskrit. (Other slightly different definitions exist.) It is called Meṣādi - "start of Aries"; this is when the equinox — where the ecliptic meets the equator — was in Aries (today it is in Pisces, 28 degrees before Aries starts). The difference between Meṣādi and the present equinox is known as Ayanāṃśa - denoting by how much of a fraction of degrees & minutes the ecliptic has progressed from its fixed (sidereal) position. Given the 25,800 year cycle for the precession of the equinoxes, the equinox was directly opposite Spica in AD 285, around the date of the Sūrya Siddhānta.[3][4]

The nakṣatras with their corresponding regions of sky are given below, following Basham.[5] As always, there are many versions with minor differences. The names on the right-hand column give roughly the correspondence of the nakṣatras to modern names of stars. Note that nakṣatras are (in this context) not just single stars but are segments on the ecliptic characterised by one or more stars. Hence more than one star is mentioned for each nakṣatra.

The Sanskrit word Yoga means "union", but in astronomical calculations it is used in the sense of "alignment". First one computes the angular distance along the ecliptic of each object, taking the ecliptic to start at Meṣa or Aries (Meṣādi, as defined above): this is called the longitude of that object. The longitude of the sun and the longitude of the moon are added, and normalized to a value ranging between 0° to 360° (if greater than 360, one subtracts 360). This sum is divided into 27 parts. Each part will now equal 800' (where ' is the symbol of the arcminute which means 1/60 of a degree). These parts are called the yogas. They are labeled:

A karaṇa is half of a tithi. To be precise, a karaṇa is the time required for the angular distance between the sun and the moon to increase in steps of 6° starting from 0°. (Compare with the definition of a tithi.)

Since the tithis are 30 in number, and since 1 tithi = 2 karaṇas, therefore one would logically expect there to be 60 karaṇas. But there are only 11 such karaṇas which fill up those slots to accommodate for those 30 tithis. There are actually 4 "fixed" (sthira) karaṇas and 7 "repeating" (cara) karaṇas.

The 4 "fixed" karaṇas are:

Śakuni (शकुनि)

Catuṣpāda (चतुष्पाद)

Nāga (नाग)

Kiṃstughna(किंस्तुघ्न)

The 7 "repeating" karaṇas are:

Vava or Bava (बव)

Valava or Bālava (बालव)

Kaulava (कौलव)

Taitila or Taitula (तैतिल)

Gara or Garaja (गरज)

Vaṇija (वणिज)

Viṣṭi (Bhadra) (भद्रा)

Now the first half of the 1st tithi (of Śukla Pakṣa) is always Kiṃtughna karaṇa. Hence thiskaraṇa' is "fixed".

Next, the 7-repeating karaṇas repeat eight times to cover the next 56 half-tithis. Thus these are the "repeating" (cara) karaṇas.

The 3 remaining half-tithis take the remaining "fixed" karaṇas in order. Thus these are also "fixed" (sthira).

Thus one gets 60 karaṇas from those 11 preset karaṇas.

The Vedic day begins at sunrise. The karaṇa at sunrise of a particular day shall be the prevailing karaṇa for the whole day.

When a new moon occurs before sunrise on a day, that day is said to be the first day of the lunar month. So it is evident that the end of the lunar month will coincide with a new moon. A lunar month has 29 or 30 days (according to the movement of the moon).

The tithi at sunrise of a day is the only label of the day. There is no running day number from the first day to the last day of the month. This has some unique results, as explained below:

Sometimes two successive days have the same tithi. In such a case, the latter is called an adhika tithi where adhika means "extra". Sometimes, one tithi may never touch a sunrise, and hence no day will be labeled by that tithi. It is then said to be a Tithi Kṣaya where Kṣaya means "loss".

Determining, which name a lunar month takes is somewhat indirect. It is based on the rāshi (Zodiac sign) into which the sun transits within a lunar month, i.e. before the new moon ending the month.

There are 12 rāśi names, there are twelve lunar month names. When the sun transits into the Meṣa rāśi in a lunar month, then the name of the lunar month is Chaitra which has both Mīna rāśi and Meṣa rāśi . When the sun transits into Vṛṣabha rāśi, then the lunar month is Vaiśākha which has both Meṣa rāśi and Vṛṣabha rāśi. So on.

If the transits of the Sun through various constellations of the zodiac (Rāśi) are used, then we get Solar months, which do not shift with reference to the Gregorian calendar. The Solar months along with the corresponding Hindu seasons and Gregorian months are:

The Sanskrit grammatical derivation of the lunar month names Chaitra etc., is: the (lunar) month which has its central full moon occurring at or near the Citrā nakṣatra is called Chaitra. Another example is let's say when Pūrṇimā occurs in or near Viśākha nakṣatra, this in turn results to the initiation of the lunar month titled Vaiśākha Māsa.[6]

The lunar months are split into two Pakṣas of 15 days. The waxing paksha is called Śukla Pakṣa, light half, and the waning paksha the Kṛṣṇa Pakṣa, dark half. There are two different systems for making the lunar calendar:

Amāvāsyanta or mukhya mana system – a month begins with a new moon and ends at new moon, mostly followed in the southern states

Pūrṇimānta or gauna mana system – a month begins with a full moon and ends at full moon, followed more in the North.

p.s. Pūrṇimānta is also known as Śuklānta Māsa. And this system is recommended by Varāhamihira.

The astronomical basis of the Hindu lunar months. Also illustrates Adhika Masa (Year 2-Bhadrapada) repeats twice; the first time the Sun moves entirely within Simha Rashi thus rendering it an Ashika Masa

When the sun does not at all transit into any rāśi but simply keeps moving within a rāśi in a lunar month (i.e. before a new moon), then that lunar month will be named according to the first upcoming transit. It will also take the epithet of adhika or "extra". For example, if a lunar month elapsed without a solar transit and the next transit is into Meṣa, then this month without transit is labeled Adhika Chaitra Māsa. The next month will be labeled according to its transit as usual and will get the epithet nija ("original") or Śuddha ("unmixed"). In the animation above, Year 2 illustrates this concept with Bhadrapada repeating twice; the first time the Sun stays entirely within Simha rashi thus resulting in an Adhika Bhakradapada.

Extra Month, or adhika māsa (māsa = lunar month in this context) falls every 32.5 months. It is also known as puruśottama māsa, so as to give it a devotional name. Thus 12 Hindu mas (māsa) is equal to approximate 356 days, while solar year have 365 or 366 (in leap year) which create difference of 9 to 10 days, which is offset every 3rd year. No adhika māsa falls during Kārtika to Māgh.

A month-long fair is celebrated in Machhegaun during adhika māsa. It is general belief that one can wash away all one's sins by taking a bath in the Machhenarayan's pond.

If the sun transits into tworāshis within a lunar month, then the month will have to be labeled by both transits and will take the epithet kṣaya or "loss". There is considered to be a "loss" because in this case, there is only one month labeled by both transits. If the sun had transited into only one raashi in a lunar month as is usual, there would have been two separate months labeled by the two transits in question.

For example, if the sun transits into Meṣa and Vṛṣabha in a lunar month, then it will be called Chaitra-Vaiśākha kṣaya-māsa. There will be no separate months labeled Chaitra and Vaiśākha.

A Kṣaya-Māsa occurs very rarely. Known gaps between occurrence of Kṣaya-Māsas are 19 and 141 years. The last was in 1983. January 15 through February 12 were Pauṣa-Māgha kṣaya-māsa. February 13 onwards was (Adhika) Phālguna.

Special Case:

If there is no solar transit in one lunar month but there are two transits in the next lunar month,

the first month will be labelled by the first transit of the second month and take the epithet Adhika and

the next month will be labelled by both its transits as is usual for a Kṣaya-Māsa

This is a very very rare occurrence. The last was in 1315. October 8 to November 5 were Kārtika Adhika-Māsa. November 6 to December 5 were Kārtika-Mārgaśīrṣa Kṣaya-Māsa. December 6 onwards was Pauṣa.

Among normal months, adhika months, and kshaya months, the earlier are considered "better" for religious purposes. That means, if a festival should fall on the 10th tithi of the Āshvayuja month (this is called Vijayadashamī) and there are two Āśvayuja (Āśvina)' months caused by the existence of anadhika Āśvayuja, the first adhika month will not see the festival, and the festival will be observed only in the second nija month. However, if the second month is āshvayuja kshaya then the festival will be observed in the first adhika month itself.

When two months are rolled into one in the case of a kshaya māsa, the festivals of both months will also be rolled into this Kṣaya Māsa'. For example, the festival of Mahāshivarātri which is to be observed on the fourteenth tithi of the Māgha Kṛṣṇa-Pakṣa was, in 1983, observed on the corresponding tithi of Pauṣa-Māgha Kṣaya Kṛṣṇa-Pakṣa, since in that year, Pauṣa and Māgha were rolled into one, as mentioned above. When two months are rolled into one in the case of a Kṣaya Māsa, the festivals of both months will also be rolled into this kṣaya māsa.

The new year day is the first day of the shukla paksha of Chaitra. In the case of adhika or kshaya months relating to Chaitra, the aforementioned religious rules apply giving rise to the following results:

If an adhika Chaitra is followed by a nija Chaitra, the new year starts with the nija Chaitra.

If an adhika Chaitra is followed by a Chaitra-Vaishākha kshaya, the new year starts with the adhika Chaitra.

If a Chaitra-Vaiśākha Kṣaya occurs with no adhika Chaitra before it, then it starts the new year.

There is another kind of lunisolar calendar which differs from the former in the way the months are named. When a full moon (instead of new moon) occurs before sunrise on a day, that day is said to be the first day of the lunar month. In this case, the end of the lunar month will coincide with a full moon. This is called the pūrṇimānta māna - full-moon-ending reckoning, as against the amānta māna - new-moon-ending reckoning used before.

This definition leads to a lot of complications:

The first pakṣa of the month will fall on Kṛṣṇa-Pakṣa whilst the second will be Śukla-Pakṣa in Pūrṇimānta system.

The new year is still on the first day of the Chaitra Śukla-Pakṣa. The subsequent Pakṣas will, for example, be:

Lunar Month
Candra Māsa

First Pakṣa

Ending (2nd) Pakṣa

Vaiśākha

Kṛṣṇa-Pakṣa

Śukla-Pakṣa

Jyaiṣṭha

Kṛṣṇa-Pakṣa

Śukla-Pakṣa

Āṣāḍha

Kṛṣṇa-Pakṣa

Śukla-Pakṣa

Śrāvaṇa

Kṛṣṇa-Pakṣa

Śukla-Pakṣa

Bhādrapada

Kṛṣṇa-Pakṣa

Śukla-Pakṣa

Āśvina

Kṛṣṇa-Pakṣa

Śukla-Pakṣa

Kārtika

Kṛṣṇa-Pakṣa

Śukla-Pakṣa

Mārgaśīrṣa

Kṛṣṇa-Pakṣa

Śukla-Pakṣa

Pauṣa

Kṛṣṇa-Pakṣa

Śukla-Pakṣa

Māgha

Kṛṣṇa-Pakṣa

Śukla-Pakṣa

Phālguna

Kṛṣṇa-Pakṣa

Śukla-Pakṣa

Chaitra

Kṛṣṇa-Pakṣa

Śukla-Pakṣa

Note:

Phālguna Māsa is the last Lunar month, with the last pakṣa of the year in this pūrṇimānta system being Phālguna Śukla-Pakṣa.

The Śukla Pakṣa of a given month, say Chaitra, comprises the same actual days in both systems, as can be deduces from a careful analysis of the rules. However, the Chaitra Kṛṣṇa-Pakṣas defined by the 2 systems will be on different days, since the Chaitra Kṛṣṇa-Pakṣa precedes the Chaitra Śukla-Pakṣa in the pūrnimānta system but follows it in the amānta system.

Though the regular months are defined by the full moon, the adhika and kṣaya lunar months are still defined by the new moon. That is, even if the pūrnimānta system is followed, adhika or kṣaya months will start with the first sunrise after the new moon, and end with the new moon.

The adhika month will therefore get sandwiched between the 2 pakṣas of the nija months. For example, a Śrāvaṇa Adhika Māsa will be inserted as follows:

nija Śrāvaṇa Kṛṣṇa-Pakṣa

adhika Śrāvaṇa Śukla-Pakṣa

adhika Śrāvaṇa Kṛṣṇa-Pakṣa and

nija Shrāvana Śukla-Pakṣa
after which Bhādrapada Kṛṣṇa-Pakṣa will follow subsequently as usual.

If there is an adhika Chaitra, then it will follow the (nija) Chaitra Krṣṇa-Pakṣa at the end of the year. Only with the nija Chaitra Śukla-Pakṣa will the new year start. The only exception is when it is followed by a kṣaya, and that will be mentioned later.

The kṣaya month is more complicated. If in the amānta system there is a Pauṣa-Māgha Kṣaya Māsa, then in the pūrnimānta system there will be the following pakṣas:

Pauṣa Kṛṣṇa-Pakṣa

Pauṣa-Maagha kshaya Śukla-Pakṣa

Māgha-Phālguna Kṣaya Kṛṣṇa-Pakṣa and a

Phālguna Śukla-Pakṣa.

The special Kṣaya case where an adhika māsa precedes a kshaya māsa gets even more convoluted. First, we should remember that the Āśvina Śukla-Pakṣa is the same in both the systems. After this come the following Pakṣas:

nija Kārtika Kṛṣṇa-Pakṣa

adhika Kārtika Śukla-Pakṣa

adhika Kārtika Kṛṣṇa-Pakṣa

Kārtika-Māgaśīrṣa Kṣaya Śukla-Pakṣa

Māgaśīrsa-Pauṣa Kṣaya Kṛṣṇa-Pakṣa

Pauṣa Śukla-Pakṣa
followed by the Māgha Kṛṣṇa-Pakṣa etc., as usual.

The considerations for the new year are:

If there is a Chaitra-Vaiśākha Kṣaya Śukla-Pakṣa:

if an adhika Chaitra' precedes it, then the adhika Chaitra Śukla-Pakṣa starts the new year

if not, the Kṣaya Śukla-Pakṣa starts the new year

If there is a Phālguna-Chaitra Kṣaya Śukla-Pakṣa then it starts the new year

However, none of these above complications cause a change in the day of religious observances. Since only the name of the Kṛṣṇa-Pakṣas of the months will change in the two systems, festivals which fall on the Kṛṣṇa-Pakṣa will be defined by the appropriate changed name. That is, the Mahāśivarātri, defined in the amānta māna to be observed on the fourteenth of the Māgha krishna paksha will now (in the pūrnimānta māna) be defined by the Phālguna krishna paksha.

A lunisolar calendar is always a calendar based on the moon's celestial motion, which in a way keeps itself close to a solar calendar based on the sun's (apparent) celestial motion.[7] That is, the lunisolar calendar's new year is to kept always close (within certain limits) to a solar calendar's new year.

Since the Hindu lunar month names are based on solar transits, and the month of Chaitra will, as defined above, always be close to the solar month of Meṣa (Aries), the Hindu lunisolar calendar will always keep in track with the Hindu solar calendar.

The Hindu solar calendar by contrast starts on April 14–15 each year. This signifies the sun's "entry" into Mesha rashi and is celebrated as the New Year in Assam, Bengal, Odisha, Manipur, Kerala, Punjab, Tamil Nadu and Tripura. The first month of the year is called "(சித்திரை)" in Tamil, "Medam" in Malayalam and Bohag in Assamese, Baisakh in Bengali/Punjabi and Nepali. This solar new year is celebrated on the same day in Myanmar, Cambodia, Laos, Nepal and Thailand.

The epoch (starting point or first day of the zeroth year) of the current era of Hindu calendar (both solar and lunisolar) is February 18, 3102 BC in the proleptic Julian calendar or January 23, 3102 BC in the proleptic Gregorian calendar. According to the Purāṇas this was the moment when Śrī Kṛṣṇa returned to his eternal abode.[8][9] Both the solar and lunisolar calendars started on this date. After that, each year is labeled by the number of years elapsed since the epoch.

This is an unusual feature of the Hindu calendar. Most systems use the current ordinal number of the year as the year label. But just as a person's true age is measured by the number of years that have elapsed starting from the date of the person's birth, the Hindu calendar measures the number of years elapsed. As of August 31, 2014[update], 5116 years have elapsed in the Hindu calendar. However, the lunisolar calendar year usually starts earlier than the solar calendar year,[citation needed] so the exact year will not begin on the same day every year.

Apart from the numbering system outlined above, there is also a cycle of 60 calendar year names, called Samvatsaras, which started at the first year (at elapsed years zero) and runs continuously:

1. Prabhava

2. Vibhava

3. Shukla

4. Pramoda

5. Prajāpati

6. Āngirasa

7. Shrīmukha

8. Bhāva

9. Yuva

10. Dhātri

11. Īshvara

12. Bahudhānya

13. Pramādhi

14. Vikrama (2000-2001)

15. Vrisha (2001-02)

16. Chitrabhānu (2002-03)

17. Svabhānu (2003-04)

18. Tārana (2004-05)

19. Pārthiva (2005-06)

20. Vyaya (2006-2007)

21. Sarvajeeth (2007-08)

22. Sarvadhāri (2008-09)

23. Virodhi (2009-10)

24. Vikrita (2010-11)

25. Khara (2011-12)

26. Nandana (2012-13)

27. Vijaya (2013-14)

28. Jaya (2014-15)

29. Manmatha (2015-16)

30. Durmukhi

31. Hevilambi

32. Vilambi

33. Vikāri

34. Shārvari

35. Plava

36. Shubhakruti

37. Sobhakruthi

38. Krodhi

39. Vishvāvasu

40. Parābhava

41. Plavanga

42. Kīlaka

43. Saumya

44. Sādhārana

45. Virodhikruthi

46. Paridhāvi

47. Pramādicha

48. Ānanda

49. Rākshasa

50. Anala

51. Pingala

52. Kālayukthi

53. Siddhārthi

54. Raudra

55. Durmathi

56. Dundubhi

57. Rudhirodgāri

58. Raktākshi

59. Krodhana

60. Akshaya

This system contains the concept of leap year also.Every 4th year will have 366 days and the others only 365.The starting point is Meshadi or Mesha Sankranti, ( 1st of the month Meṣa or the Hindu solar new year).It is also calculated a day by day mode.beginning from 1 presently it runs 1864000+.... days.This means these much days have passed in the present Kaliyuga (1/10 of Catur-Yuga's total)

They are often translated into English as the Golden, Silver, Bronze and Iron Ages, respectively. The ages follow a gradual decline of dharma, wisdom, knowledge, intellectual capability, life span and emotional and physical strength. The Kali Yuga began approximately five thousand years ago, and it has a duration of 432,000 years. The Dvāpara, Tretā, and Kṛta Yugas are two, three, and four times the length of the Kali Yuga, respectively. Thus, the ages together constitute a 1,200,000 year period—half the time required for the Sun to orbit the Galactic Sun which resides at the centre of the galaxy.

A thousand and a thousand (i.e. two thousand) Catur-Yugas are said to be one day and night of the creator Brahmā. Brahmā lives for 100 years of 360 "days" and at the end, he is said to dissolve, along with his entire Creation, into the Eternal Soul or Paramātman.

The Hindu Calendar descends from the Vedic times. There are many references to calendrics in the Vedas. The (6) Vedāṅgas (auto Veda) called Jyotiṣa (literally, "celestial body study") prescribed all the aspects of the Hindu calendars. After the Vedic period, there were many scholars such as Āryabhaṭa (5th century), Varāhamihira (6th century) and Bhāskara (12th century) who were experts scholars in Jyotiṣa and contributed to the development of the Hindu Calendar.

The most widely used authoritative text for the Hindu Calendars is the "Sūrya Siddhānta", a text of uncertain age, though some place it at 10th century.

The traditional Vedic calendar used to start with the month of agrahayan (agra=first + ayan = travel of the sun, equinox) or Mārgaśīṣa. This is the month where the Sun crosses the equator, i.e. the vernal equinox. This month was called mārgashirsha after the fifth nakshatra (around lambda orionis). Due to the precession of the Earth's axis, the vernal equinox is now in Pisces, and corresponds to the month of chaitra. This shift over the years is what has led to various calendar reforms in different regions to assert different months as the start month for the year. Thus, some calendars (e.g. Vikram) start with Chaitra, which is the present-day month of the vernal equinox, as the first month. Others may start with Vaiśākha (e.g. Bangabda). The shift in the vernal equinox by nearly four months from Agrahāyaṇa to Chaitra in sidereal terms seems to indicate that the original naming conventions may date to the fourth or fifth millennium BC, since the period of precession in the Earth's axis is about 25,800 years.

The Indian Calendar Reform Committee, appointed in 1952, identified more than thirty well-developed calendars, all variants of the Surya Siddhanta calendar outlined here, in systematic use across different parts of India. These include the widespread Vikrama and Shalivahana calendars and regional variations thereof. The Tamil calendar, a solar calendar, is used in Tamil Nadu and Kollavarsham Calendar is used in Kerala.

Both the Vikrama and the Shalivahana are lunisolar calendars, and feature annual cycles of twelve lunar months, each month divided into two phases: the 'bright half' (Śukla Pakṣa) and the 'dark half' (Kṛṣṇa Pakṣa); these correspond respectively to the periods of the 'waxing' and the 'waning' of the moon. Thus, the period beginning from the first day after the new moon and ending on the full moon day constitutes the Śukla Pakṣa, 'bright part' of the month; the period beginning from the day after Pūrṇimā (the full moon) until and including the next new moon day constitutes the Kṛṣṇa Pakṣa, the'dark part' of the month.

The names of the 12 months, as also their sequence, are the same in both calendars; however, the new year is celebrated at separate points during the year and the "year zero" for the two calendars is different. In the Vikrama calendar, the zero year corresponds to 56 BC, while in the Shalivahana calendar, it corresponds to AD 78. The Vikrama calendar begins with the month of Baiśākha or Vaiśākha (April), or Kartak (October/November) in Gujarat. The Shalivahana calendar begins with the month of Chaitra (March) and the Ugadi/Gudi Padwa festivals mark the new year.

Another little-known difference between the two calendars exists: while each month in the Shalivahana calendar begins with the 'bright half' and is followed by the 'dark half', the opposite obtains in the Vikrama calendar. Thus, each month of the Shalivahana calendar ends with the no-moon day and the new month begins on the day after that, while the full-moon day brings each month of the Vikrama calendar to a close (This is an exception in Gujarati Calendar, its month (and hence new year) starts on a sunrise of the day after new moon, and ends on the new moon, though it follows Vikram Samvat).

In Gujarat, Diwali is held on the final day of the Vikram Calendar and the next day marks the beginning of the New Year and is also referred as ‘Annakut’ or Nutan Varsh or Bestu Varash. In the Hindu calendar popularly used in North India the year begins with Chaitra Shukala Pratipadha (March – April).

Indian months are listed below, numbered according to the Shaka calendar. Shaka and Chaitradi Vikram (UP, Rajasthan, Maharashtra etc.) start with Chaitra (The first month of the year is called "Chitterai (चैत्र)" in Marathi) Kartikadi Vikram (Gujarat) start in Kartika.

Years are synchronized with the solar sidereal year by adding a month every three years. The extra month is termed as "Adhik Mass" (extra month). This extra month is called Mala Masa (impure month) in Eastern India.

In Bihar, Uttar Pradesh, Rajasthan, and many northern region of India months are Purnimanta (means month ends on Purnima or Full Moon). In Gujarat, Maharashtra, and other parts of many south Indian region, months are Amanta (months end on Amavasya).

A variant of the Shalivahana Calendar was reformed and standardized as the Indian National calendar in 1957. This official calendar follows the Shalivahan Shak calendar in beginning from the month of Chaitra and counting years with AD 78 being year zero. It features a constant number of days in every month (with leap years).